Abstract:Spectral localization is intrinsically unstable under perturbation. As a result, the adiabatic theorem of quantum mechanics cannot generally hold for localized eigenstates. However, it turns out that a remnant of the adiabatic theorem, which we name the "locobatic theorem", survives: The physical evolution of a typical eigenstate ψ for a random system remains close, with high probability, to the spectral flow for ψ associated with a restriction of the full Hamiltonian to a region where ψ is supported. We make … Show more
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